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Suppose A=[{:(a,b),(c,d):}] is real mat...

Suppose `A=[{:(a,b),(c,d):}]` is real matrix with nonzero entries, ad-bc=0 , and `A^(2)`=A. Then a+d equals

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1

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The correct Answer is:
A
`A^(2)=[{:(a,b),(c,d):}][{:(a,d),(c,d):}] ad =bc implies (a)/(b)=(c)/(d)=k`
`=[{:(a^(2)+bc,ab+bd),(ac+cd,bc+d^(2)):}] a=bk,c=dk`
`a^(2)+bc=a ,b(a+d)=b`
`impliesa+d=1`
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